materials selection - mit opencourseware · pdf filematerials selection. objective • aim...
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Unified Engineering
Lecture M21 12/2/2003
Materials Selection
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Objective• Aim to provide coherent overview of material selection
– Materials (and structural configurations and processes) should be selected for applications based on measurable criteria
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Key Ideas• It is possible to compare the suitability of materials for a
given application according to quantifiable performance metrics based on material properties
– Properties (such as Young’s modulus, density,strength) quantify material performance
• Some materials properties are more invariant than others
– Role of scale, role of manufacturing, microstructure
– Fiber composite allow flexibility
– Important to know what you can change - or not!
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Central Problem - Interaction ofFunction, Material, Process and Shape
Function Transmits loads, heat
resonates, contains pressurestores energy etc.
At minimum weight, cost, size,or maximum efficiency,
safety etc.(rest of Unified)
Material Shape
Process
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References
• Material Selection in Mechanical Design, M.F Ashby, Pergamon Press, Oxford, 1992
• Ashby and Jones, Engineering Materials I, Chapter 6
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Materials for Mechanical Elements- performance indices
• Design of a structural element is specified by three parameters, or groups of parameters (performance indices):
– Functional requirements (F), Geometry (G) and
Material Properties (M)
• We can quantify the interdependence if we can specify performance, p, as a function of F, G and M:
» p = f(F, G, M)
• We can simplify further if the three groups of parameters are separable, i.e:
» p = f1(F) . f2(G) . f3(M)
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Ex: Lightweight stiff rod - tensile loadP P
AL Material, modulus E, density r - note these are a property of the material, and cannot be independently selected
• Mass of rod given by m = rALAE • Stiffness of rod, given by k =
P =
d L • Combining, by eliminating free variable, A:
r r m =
kL2
= k ⋅L2 ⋅ E E
F G M
Choose material with low r/E ratio!!!
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MATERIAL SELECTION FOR AMICROMECHANICAL RESONATOR
Fatigue test device (Courtesy of Stuart Brown. Used with permission.)
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Example 2 - High f Beam Resonator d = A0 sinwt
L 4
I =pr
Material, modulus E, density r 4
• Natural (resonant) frequency, f EI Er2 E r = f ( B.C' s)⋅ bnf µ ML3 fi b1 L4 = b2 L2 r r
• For high frequency resonator select high E/r
• Note frequency f µ 1
for given r implies scale effectL L
Choose material with low r/E ratio, MEMS allow high frequencies
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MODULUS - DENSITY RATIOS OFSOME MEMS MATERIALS
Material Density, r,
Kg/m3
Modulus, E,
GPa
E/ r
GN/kg-m Silicon 2330 165 72
Silicon Oxide 2200 73 36
Silicon Nitride 3300 304 92
Nickel 8900 207 23
Aluminum 2710 69 25
Aluminum Oxide
3970 393 99
Silicon Carbide 3300 430 130
Diamond 3510 1035 295
Silicon performs well, diamond, SiC and SiN significantly better
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DEFLECTION OF CIRCULAR PLATE
0.67 mga2 2d = m = pa tr
p Et 3 2a
δ t
mg
The elastic deflection of a telescope mirror (shown as a flat disc), under its own weight. (Adapted from Ashby.)
Ê0.67/ gˆ1 2 pa 4 Á
Ê r 3 ̂ 1 2 r 3
m = Á ˜ M = Ë d ¯ Á
Ë E ˜̃ E¯
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Example 3 - Telescope Mirror3 r
• Choose materials with high M = E
The distortion of the mirror under its own weight can be corrected by applying forces to the back surface. (Adapted from Ashby.)
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MODULUS - DENSITY PROPERTY MAP
Note contours of equal performance
A shby
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STRENGTH-MODULUS PROPERTY MAP
Might also want Deflection at minimum force -polymers would appear more attractive
A shby
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STRENGTH-DENSITY MAP
Ashby
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CTE-THERMAL CONDUCTIVITY
Ashby
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CTE-MODULUS MAP
Determines thermal stress, thermal buckling limits for thin tethers,
also
Feasibility of thermal actuation
Ashby
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SUMMARY• Aimed to provide coherent overview of material selection
– Materials (and structural configurations and processes) should be selected for applications based on measurable criteria
– Often combinations of material properties
• Material properties group according to class of material
– Metal, ceramic, polymers
– Engineered materials (composites, foams)
– Natural materials (wood, bone, etc)